Coefficient estimates for some families of bi-Bazilevič functions of the Ma-Minda type involving the Hohlov operator

Abstract

In this paper, we introduce and investigate a new subclass of the function class Σ of biunivalent functions of the Bazilevic type defined in the open unit disk, which are associated with the Hohlov operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a 2 | and |a 3 | for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. (2010): Primary 30C45; Secondary 30C50. Mathematics subject classification

Coefficient estimates for a new subclass of analytic and bi-univalent functions by Hadamard product

“…In this work, we introduce a new subclass of bi-univalent functions which is defined by Hadamard product and find upper bounds for the second and third coefficients for functions in this new subclass. Besides, the estimates on the coefficients |a 2 | and |a 3 | presented in this work would generalize and improve some of results of Aouf et al [4], Bulut [8], Ç aglar et al [9], El-Ashwah [12], Frasin and Aouf [14], Murugusundaramoorthy [18], Orhan et al [19], Porwal and Darus [20], Prema and Keerthi [21], Srivastava et al [24], Srivastava et al [25] and related works in this literature.…”

Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions

“…In the …nal section, using the Faber polynomial expansion we found upper bounds for ja n j (n 3) coe¢ cients of functions in the class de…ned by De…nition 1.1, and then we obtained an estimate for the initial coe¢ cients ja 2 j for the functions of this class. Thus, regarding the proofs of the Theorems 3.1 and 3.2, this technique can be applied for all classes that are de…ned similarly to the De…nition 1.1 in diverse papers enhancing their outcomes (see for example [3,10,21,23,28] and references therein).…”

Bi-Bazilevič functions of complex order involving Ruscheweyh type q-difference operator

“…Many researchers (see [1,7,9,17]) have recently introduced and investigated several interesting subclasses of the biunivalent function class Σ. Motivated by the earlier work of Bulut [5], Deniz [6], Inayat Noor [10] and Srivastava et al [16], in the present paper we introduce new families of Bazilevic functions of complex order of the function class Σ, involving the operator D q (R δ q f (z)), and find estimates on the coefficients |a 2 | and |a 3 | for functions in the new subclass of function class Σ. Several related classes are also considered, and connection to earlier known results are made.…”

“…Then p(z) and q(z) are analytic in with p(0) = 1 = q(0). Since u, v : → , the functions p(z) and q(z) have a positive real part in , and |p k | ≤ 2 and |q k | ≤ 2 for each k. Using (15) and (16) in (13) and (14) respectively, we have…”